If somebody is travelling at a different speed or direction than you, they will disagree with you on whether certain events happened at the same time.

If something is moving very fast, it gets shorter in the direction that it is moving.

Today we will talk about the twin paradox, an idea that can be very confusing, but very interesting.

How Can Both People Have Their Time Slowed Down?

Relativity says that if somebody is moving very fast compared to you, you will observe their clock slowing down. The faster they go, the slower their clocks will tick. If a car drove by you at close to the speed of light, everybody inside would look like they were moving very slowly, even though the car would be moving very fast.

But what would happen if you were inside the car that was travelling close to the speed of light? Then it would look like the houses and the street and the telephone poles were moving past your car at close to the speed of light. They would be moving close to the speed of light relative to you.

But if that’s true, then shouldn’t everybody else’s time be slowed down? Shouldn’t the people in their houses and the dog on the street be moving around really slow, almost like they were frozen in time?

Yes.

But that is very strange, isn’t it? How can it be true that when you are in the car, everybody else seems like they are frozen in time, but when they look at you, it looks like you are the one who is frozen in time?

This is very confusing, and it took Einstein to figure out that this could be true and that somehow it would all make sense.

What One Person Calls Time, Another Person Will Call Distance

Let’s pretend that the speed of light is very slow, and your mom is driving you to the store and back at close to the speed of light. Let’s say that your car’s clock says that the trip takes half an hour. But when you get home, you notice that the clock at your house says that a whole hour has gone by. How did this happen?

Well, when you are riding in your car, everything is moving past you at close to the speed of light. Since it is moving close to the speed of light, it also shrinks in the direction it is moving. This means that the road shrinks, and the distance to the store shrinks. So you only have to drive half as far to get to the store and back! It only takes half an hour.

But if somebody was watching your mom drive you around, they would see something different. The road doesn’t shrink. Instead, your clock slows down. It takes twice as long for it to tick. According to them, the trip really took an hour. It just seemed like it took half an hour to you, because your clock was ticking slower!

This may be very strange, but both of you would be right. According to you, the distance shrank and it took less time to drive to the store and back. According to somebody watching you drive around, your clock was ticking slow, so it records less time as you drive to the store and back. Both of these answers are right.

But What About Your Clock At Home?

Well, that explains why the trip takes less time for you, but it still doesn’t explain your clock at home.

When you are driving around at close to the speed of light, it means that your clock at home is moving around at close to the speed of light compared to you. That should mean that your clock at home should tick slower, not faster.

If your clock at home is ticking slower than your clock in the car, why does it say that the trip took an hour, when your clock in the car says it only took half an hour? That’s backwards!

Remember last week when we talked about how not everybody will agree on when certain things happen at the same time? Well, it turns out that this is the perfect solution.

If you are moving in one direction, and you see two things happen at the same time, then if somebody is moving in a different direction, they will see those things happen at different times. Go back and read the post again if you don’t understand why.

So here is how it happens. As you drive away from your home, you know that your clock at home is moving close to the speed of light compared to you, so it is ticking twice as slow as the clock in your car.

By the time you get to the store, the clock in your car says you have been driving for 15 minutes, but you know that the clock back at home has only been ticking for 7 and a half minutes.

But then, you turn around and start driving back home.

And there’s the answer, right there!

When you turn around, you are moving in a different direction. That means you can’t agree with what you were saying earlier about certain things happening at the same time.

When you were driving toward the store, you knew that you got to the store at the same time that your clock at home said 7 and a half minutes had gone by.

Now that you are moving in the opposite direction, you can’t say this anymore. Instead, you will say that when you got to the store, your clock at home said that you were gone for almost an hour! Seven and a half minutes less than an hour, to be exact.

So then, as you drive home, you know that your clock at home is still ticking half as slow as the clock in your car, but it has skipped ahead. By the time you get home, your clock at home will say an hour has gone by, even though the clock in your car says it has only been half an hour!

And that is the solution to the twin paradox. If this is hard for you to understand, that’s okay. Einstein struggled with these ideas for years before he was sure he had the right answer. You might need to read through these posts more than once before you feel like you really understand it. There’s nothing wrong with that.